Cvx Your Objective Function Is Not A Scalar.

7 min read Sep 30, 2024

"cvx: Your Objective Function is Not a Scalar" - A Guide to Troubleshooting This Error

CVX, a powerful modeling framework for convex optimization problems, offers a robust environment for tackling complex mathematical problems. However, during your journey with CVX, you might encounter the dreaded error message: "cvx: Your objective function is not a scalar." This message signals an issue with the objective function you've defined, indicating that it's not returning a single value as expected.

This error can be perplexing, but fear not! This guide will break down the root causes, equip you with troubleshooting strategies, and provide clear examples to ensure you successfully navigate this obstacle.

Understanding the Problem

At its core, the "cvx: Your objective function is not a scalar." error arises when CVX expects a single numerical value (scalar) to represent the objective function's output, but instead, it encounters a vector or matrix. This mismatch disrupts the optimization process, as CVX relies on minimizing or maximizing a scalar value to find the optimal solution.

Common Causes of the Error

Let's delve into the most frequent scenarios that lead to this error:

Vector or Matrix as Objective Function: Your objective function is defined using an expression that returns a vector or matrix instead of a scalar. CVX requires a single numerical value to represent the objective, not a collection of values.
Incorrect Indexing: When referencing elements within vectors or matrices within the objective function, you may be accidentally accessing multiple elements, resulting in a vector or matrix output.
Improper Use of Element-wise Operations: Using operators like .* (element-wise multiplication), ./ (element-wise division), or .^ (element-wise exponentiation) on matrices or vectors can inadvertently create a matrix or vector output, causing the error.

Troubleshooting Strategies

Here's a step-by-step guide to diagnose and resolve the "cvx: Your objective function is not a scalar." error:

Inspect Your Objective Function: Carefully examine the expression defining your objective function. Identify all variables and operations involved. Pay close attention to indexing and element-wise operators.
Verify Variable Dimensions: Ensure that all variables used within the objective function are either scalars or correctly defined vectors or matrices. Incorrect dimensions can lead to the error.
Check Indexing: Double-check indexing within the objective function. Ensure that you are indexing correctly to access single elements (scalars) if necessary.
Avoid Element-wise Operations: Minimize the use of element-wise operators like .*, ./, and .^ within the objective function. If necessary, use matrix multiplication (*) or division (/) to achieve the desired results.
Use sum() or trace(): If you need to combine values from a vector or matrix into a single scalar, utilize the sum() or trace() functions. sum() sums all elements of a vector or matrix, while trace() sums the diagonal elements of a matrix.

Example:

Let's consider a simple example to illustrate the error and its resolution. Imagine you want to minimize the sum of squared errors for a linear regression problem:

% Incorrect Objective Function (vector output)
cvx_begin
    variable x(n);
    minimize( sum((y - A*x).^2) ); 
cvx_end

% Corrected Objective Function (scalar output)
cvx_begin
    variable x(n);
    minimize( sum(sum((y - A*x).^2)) ); 
cvx_end

In the incorrect version, the expression (y - A*x).^2 results in a vector of squared errors. The sum() function operates on each element of the vector, but the output is still a vector.

By adding another sum() function, we now sum the elements of the error vector, producing a scalar value, thus resolving the "cvx: Your objective function is not a scalar." error.

Conclusion

The "cvx: Your objective function is not a scalar." error is a common hurdle encountered in CVX optimization. By diligently analyzing your objective function, paying attention to variable dimensions, indexing, and element-wise operations, you can effectively pinpoint and resolve the cause of the error. Remember, the key is to ensure that your objective function returns a single scalar value, enabling CVX to effectively optimize your problem.

Cvx Your Objective Function Is Not A Scalar.